An important notion in the theory is that of a hook in a diagram
(see [1]} for more on this).
The hook \(H_{ij}\)  to \((i,j)\in Y(\lambda )\)  is the set of boxes
\(H_{ij}(\lambda ) = \lbrace (i,s) \mid s\in \lbrace j,\ldots ,\lambda _i\rbrace \rbrace \cup \lbrace (r,j) \mid r\in \lbrace i,\ldots ,\lambda ^t_j\rbrace \rbrace ;\) 
